Example image of eyePlorer eyePlorer map for 'Orthogonal group': Group (mathematics) Mathematics Matrix multiplication Orthogonal matrix General linear group Subgroup Transpose Linear map Quadratic form Cartan–Dieudonné theorem Determinant Normal subgroup Characteristic (algebra) Index of a subgroup Kernel (matrix) Algebraic group Invertible matrix Real number Compact space Connected space Dimension Identity component Identity matrix Lie group Euclidean group Isometry N-sphere Sphere Orientation (mathematics) Characteristic subgroup Direct product Cyclic group Rotation Coordinate rotations and reflections Coxeter group Length function Longest element of a Coxeter group Reflection through the origin Absolute value Circle Circle group Complex number Dihedral group Symmetry group Rotation group Algebraic topology Covering space Fundamental group Spin group Real line